论文标题
有限加权图中的Bakry-Émery曲率清晰度和曲率流。 ii。执行
Bakry-Émery curvature sharpness and curvature flow in finite weighted graphs. II. Implementation
论文作者
论文摘要
在两篇论文序列的第二部分中，我们讨论了基于Bakry-émery计算的加权图上曲率流的实现。可以对此流程进行调整以保留马尔可夫的特性，并且随着时间的流逝，它的限制变成了曲率尖锐的加权图。在回顾了与理论方面有关的第一篇论文的一些主要结果之后，我们提出了各种示例（随机图，路径，周期，完整的图，楔形总和和完整图形的笛卡尔产品，超级管道），并展示此流量的进一步特性。在我们的研究中，一个特殊的方面是渐近稳定性和曲率流量平衡的不稳定性。本文以辅助文件中可用的Python功能和例程的描述结尾。我们希望通过示例对Python实施的解释将有助于用户进行自己的曲率流实验。
In this second part of a sequence of two papers, we discuss the implementation of a curvature flow on weighted graphs based on the Bakry-Émery calculus. This flow can be adapted to preserve the Markovian property and its limits as time goes to infinity turn out to be curvature sharp weighted graphs. After reviewing some of the main results of the first paper concerned with the theoretical aspects, we present various examples (random graphs, paths, cycles, complete graphs, wedge sums and Cartesian products of complete graphs, hypercubes) and exhibit further properties of this flow. One particular aspect in our investigations is asymptotic stability and instability of curvature flow equilibria. The paper ends with a description of the available Python functions and routines available in the ancillary file. We hope that the explanations of the Python implementation via examples will help users to carry out their own curvature flow experiments.
